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Mathematical logic and quantum finite state automata

Ilze Dzelme-Bērziņa
2009 Theoretical Computer Science  
paper is a review of the connection between formulas of logic and quantum finitestate automata in respect to the language recognition and acceptance probability of quantum finite-state automata.  ...  a r t i c l e i n f o Keywords: Quantum finite-state automata First-order logic Modular logic Measure-once quantum finite-state automata Measure-many quantum finite-state automata a b s t r a c t This  ...  Acknowledgement The author's research has been supported by the European Social Fund.  ... 
doi:10.1016/j.tcs.2009.01.030 fatcat:zdl3krm4jjcojklohpgopgvrqq

Multihead two-way probabilistic finite automata [chapter]

Ioan I. Macarie
1995 Lecture Notes in Computer Science  
Partially based on this relation, we find an apparently easier logspace complete problem for PL (the class of languages recognized by logspace unbounded-error probabilistic Turing machines), and we discuss  ...  We define multihead probabilistic finite automata with logspace constructible transition probabilities, and we describe a technique to simulate these automata by standard logspace probabilistic Turing  ...  Moreover, NL is logspace reducible to the class of languages recognized by two-head one-way nondeterministic finite automata [Sul] .  ... 
doi:10.1007/3-540-59175-3_103 fatcat:l37vry5hunb3nk5dghikepjwia

Beyond omega-Regular Languages

Mikolaj Bojanczyk, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
The class of ω-regular languages carries over to ω-words many of the good properties of regular languages of finite words.  ...  For a language L ⊆ A ω , call two finite words L-equivalent if they can be  ...  Above, we have described several classes of languages of ω-words, defined by: the logics with new quantifiers and automata with counters.  ... 
doi:10.4230/lipics.stacs.2010.2440 dblp:conf/stacs/Bojanczyk10 fatcat:6oaslsh6kndxzixfk6zzpwqj7m

Quantum finite automata: survey, status and research directions [article]

Amandeep Singh Bhatia, Ajay Kumar
2019 arXiv   pre-print
This article seeks to provide a comprehensive and systematic analysis of quantum finite automata models, quantum finite automata models with density operators and quantum finite automata models with classical  ...  In light of the current state of quantum computation theory research, a systematic review of the literature seems timely.  ...  Acknowledgments Amandeep Singh Bhatia was supported by Maulana Azad National Fellowship (MANF), funded by Ministry of Minority Affairs, Government of India.  ... 
arXiv:1901.07992v1 fatcat:yoxwrd6e55gh3heapwy3w5uuhm

Varieties Generated by Certain Models of Reversible Finite Automata [chapter]

Marats Golovkins, Jean-Eric Pin
2006 Lecture Notes in Computer Science  
Consequently, we obtain a characterization of the boolean closure of the classes of languages recognized by these models.  ...  Reversible finite automata with halting states (RFA) were first considered by Ambainis and Freivalds to facilitate the research of Kondacs-Watrous quantum finite automata.  ...  Reversible Finite Automata The class of languages recognized by CRFA (which, by Proposition 2.3, is also the class of languages recognized by RFA) will be denoted by K.  ... 
doi:10.1007/11809678_11 fatcat:7jp2nrcxv5dirmzgvpe4lhxlju

Postselection Finite Quantum Automata [chapter]

Oksana Scegulnaja-Dubrovska, Lelde Lāce, Rūsiņš Freivalds
2010 Lecture Notes in Computer Science  
At first we prove by a direct construction that the complement of this language can be recognized this way.  ...  There are several nonequivalent definitions of quantum finite automata. Nearly all of them recognize only regular languages but not all regular languages.  ...  The first results on MM-quantum finite automata were obtained by Kondacs and Watrous [21] . They showed that the class of languages recognized by QFAs is a proper subset of regular languages.  ... 
doi:10.1007/978-3-642-13523-1_14 fatcat:aqkjzy3v7va3bpzdsic3ysb6zy

Language Classes Associated with Automata Over Matrix Groups [article]

Özlem Salehi, Flavio D'Alessandro, A.C.Cem Say
2016 arXiv   pre-print
We investigate the language classes recognized by group automata over matrix groups. We present a summary of the results obtained so far together with a number of new results.  ...  We look at the computational power of time-bounded group automata where the group under consideration has polynomial growth.  ...  We present some new results about the classes of languages recognized by finite automata over matrix groups.  ... 
arXiv:1609.00396v1 fatcat:5rt4rrakjbdd7jsdfbfjs2eto4

On the Size Complexity of Deterministic Frequency Automata [chapter]

Rūsiņš Freivalds, Thomas Zeugmann, Grant R. Pogosyan
2013 Lecture Notes in Computer Science  
First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared.  ...  Then approximations of a language are considered, where a language L is called an approximation of a language L if L differs from L in only a finite number of strings.  ...  The research was supported by Grant No. 09.1570 from the Latvian Council of Science and the Invitation Fellowship for Research in Japan S12052 by the Japan Society for the Promotion of Science.  ... 
doi:10.1007/978-3-642-37064-9_26 fatcat:4vk4iuhrnvf5toudzfzngmtgzm

Residual Finite Tree Automata [article]

J. Carme, A. Lemay (INRIA Futurs), A. Terlutte
2006 arXiv   pre-print
In the top-down case, we obtain a subclass of regular tree languages which contains the class of languages recognized by deterministic top-down tree automata.  ...  In this paper, we define new classes of non deterministic tree automata, namely residual finite tree automata (RFTA).  ...  As a consequence, ↑-RFTA have the same expressive power than finite tree automata: Theorem 1. The class of tree languages recognized by ↑-RFTA is the class of regular tree languages.  ... 
arXiv:cs/0609015v1 fatcat:v4c7udg3xbcypp7ui2ht6eipqu

Residual Finite Tree Automata [chapter]

Julien Carme, Rémi Gilleron, Aurélien Lemay, Alain Terlutte, Marc Tommasi
2003 Lecture Notes in Computer Science  
In the top-down case, we obtain a subclass of regular tree languages which contains the class of languages recognized by deterministic top-down tree automata.  ...  In this paper, we define new classes of non deterministic tree automata, namely residual finite tree automata (RFTA).  ...  As a consequence, ↑-RFTA have the same expressive power than finite tree automata: Theorem 1. The class of tree languages recognized by ↑-RFTA is the class of regular tree languages.  ... 
doi:10.1007/3-540-45007-6_13 fatcat:xbseotzomfbwppa4lfshrqjmiy

Page 2097 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
Summary: “We analyze the minimization problem for determin- istic weak automata, a subclass of deterministic Biichi automata, which recognize the regular languages that are recognizable by de- terministic  ...  Finally, the time complexity of the algorithm is given in terms of the numbers of states of minimal multi-automata recognizing the rational languages A, B and K.  ... 

Language Classes Associated With Automata Over Matrix Groups [article]

Özlem Salehi, Flavio D'Alessandro, A. C. Cem Say
2018 arXiv   pre-print
We investigate the language classes recognized by group automata over matrix groups.  ...  We also introduce the notion of time complexity for group automata and demonstrate some separations among related classes.  ...  The class of regular languages is characterized as the set of languages recognized by finite automata over the trivial group F 0 in [5] .  ... 
arXiv:1810.12415v2 fatcat:x3sjic4skrg55kzuxoi5vrwm3q

Operations on Weakly Recognizing Morphisms [chapter]

Lukas Fleischer, Manfred Kufleitner
2016 Lecture Notes in Computer Science  
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such  ...  a morphism if and only if it is accepted by some Büchi automaton.  ...  We thank the anonymous referees for several useful suggestions which helped to improve the presentation of this paper.  ... 
doi:10.1007/978-3-319-41114-9_10 fatcat:ykhj7ovl4ffvra43xbwzyigjya

Extended Models of Finite Automata [article]

Özlem Salehi
2019 arXiv   pre-print
We investigate the language recognition power of finite automata over integer and rational matrix groups and reveal new relationships between the language classes corresponding to these models.  ...  A finite automaton over a group G is a nondeterministic finite automaton equipped with a register that holds an element of the group G.  ...  automata is a proper superset of the class of languages recognized by extended finite automata. • Over the monoid of 3 × 3 integer matrices, the class of languages recognized by one-way nondeterministic  ... 
arXiv:1912.11699v1 fatcat:umb4afgbhzatratlrleuvnrmmm

What You Must Remember When Processing Data Words

Michael Benedikt, Clemens Ley, Gabriele Puppis
2010 Alberto Mendelzon Workshop on Foundations of Data Management  
We provide a Myhill-Nerode-like theorem that characterizes the class of data languages recognized by deterministic finite-memory automata (DMA).  ...  As a byproduct of this characterization result, we obtain a canonical representation for any DMA-recognizable language.  ...  Using this we can give a characterization of the class of languages recognized by some DMA, which closely resembles the Myhill-Nerode theorem.  ... 
dblp:conf/amw/BenediktLP10 fatcat:u5mbcviy6bgi5dgbgqjdtkabs4
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